Resource allocation in multiantenna systems-achieving max-min fairness by optimizing a sum of inverse SIR

We address the problem of jointly optimizing transmit powers and linear preequalizers (e.g., beamformers) for a multiuser downlink channel. All results can be transferred to the dual uplink channel. The link quality of each user is determined by the signal-to-interference ratio (SIR). Two common strategies for distributing the system resources by joint optimization of transmit powers and beamformers are: 1) maximize the minimum SIR, to which we refer as max-min fairness, and 2) minimize the sum of weighted inverse SIR. Both strategies are generally not equivalent. In this paper, it is shown how the weighting factors should be chosen so that the sum optimization approach achieves optimal max-min fairness. An efficient iterative algorithm is proposed for solving this nonlinear optimization problem. Monotonicity and convergence are proved.